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We develop a Trust Region method with Regularized Barzilai-Borwein step-size obtained in a previous paper for solving large-scale unconstrained optimization problems. Simultaneously, the non-monotone technique is combined to formulate an…

Optimization and Control · Mathematics 2024-09-24 Xin Xu , Congpei An

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…

Optimization and Control · Mathematics 2026-02-16 Hanfeng Zeng , Wenqing Ouyang , Andre Milzarek

In this work we present TRFD, a derivative-free trust-region method based on finite differences for minimizing composite functions of the form $f(x)=h(F(x))$, where $F$ is a black-box function assumed to have a Lipschitz continuous…

Optimization and Control · Mathematics 2025-10-23 Dânâ Davar , Geovani Nunes Grapiglia

Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…

Optimization and Control · Mathematics 2022-01-05 Shigeng Sun , Jorge Nocedal

This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is…

Optimization and Control · Mathematics 2015-01-12 Masoud Ahookhosh , Susan Ghaderi

We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence of unconstrained nonsmooth barrier subproblems. We use a variant of the proximal…

Optimization and Control · Mathematics 2024-02-29 Geoffroy Leconte , Dominique Orban

In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…

Optimization and Control · Mathematics 2013-04-11 Afonso S. Bandeira , Katya Scheinberg , Luis Nunes Vicente

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…

Optimization and Control · Mathematics 2018-06-27 Frank E. Curtis , Katya Scheinberg , Rui Shi

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep…

Optimization and Control · Mathematics 2024-01-18 Natasa Krejic , Natasa Krklec Jerinkic , Angeles Martinez , Mahsa Yousefi

In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for…

Optimization and Control · Mathematics 2021-05-11 Ahmad Kamandi , Keyvan Amini

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…

Optimization and Control · Mathematics 2022-01-03 S. Bellavia , G. Gurioli , B. Morini , Ph. L. Toint

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…

Optimization and Control · Mathematics 2024-11-05 Jelena Diakonikolas , Cristóbal Guzmán

The trust-region (TR) method is renowned historically for its robustness in nonconvex problems and extraordinary numerical performance, but the study of its performance in convex optimization is somehow limited. This paper complements the…

Optimization and Control · Mathematics 2026-01-26 Yuntian Jiang , Chang He , Chuwen Zhang , Dongdong Ge , Bo Jiang , Yinyu Ye

We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…

Optimization and Control · Mathematics 2024-05-24 Tianshu Wen , Matthew J. Zahr

We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…

Optimization and Control · Mathematics 2021-08-04 Aleksandr Y. Aravkin , Robert Baraldi , Dominique Orban

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…

Optimization and Control · Mathematics 2026-05-12 Mitsuaki Obara , Takayuki Okuno , Akiko Takeda

In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…

Optimization and Control · Mathematics 2025-09-10 Suprova Ghosh , Debdas Ghosh , Christiane Tammer , Xiaopeng Zhao

In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical…

Optimization and Control · Mathematics 2026-01-15 Leandro Farias Maia , Robert Baraldi , Drew P. Kouri

Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…

Optimization and Control · Mathematics 2026-04-16 Aike Yang , Hao Wang